Elearning 1-23 Review of Sine and Cosine graphs

Front

What is the vertical shift in a sine or cosine function?

Back

The vertical shift indicates how much the graph of the function is moved up or down from its standard position. For example, a vertical shift of 'Down 3' means the entire graph is shifted 3 units downward.

Front

What is the period of a cosine function?

Back

The period of a cosine function is the distance along the x-axis for one complete cycle of the wave. For the function y=7cos(6x), the period is calculated as 2π divided by the coefficient of x, which is 6, resulting in a period of π/3.

Front

How do you determine the equation of a cosine function from its graph?

Back

To determine the equation of a cosine function, identify the amplitude, period, and vertical shift from the graph. For example, if the graph shows a maximum value of 2 and a minimum of -2, the amplitude is 2, leading to an equation like y=2cos(x) if there is no vertical shift.

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is represented by the coefficient in front of the sine or cosine function.

Front

How do you write the equation of a sine function with a specific period and amplitude?

Back

To write the equation of a sine function, use the formula y = A sin(Bx), where A is the amplitude and B is related to the period. For a period of 4π and amplitude of 5, the equation is y = 5sin(½x).

Front

What does a negative coefficient in front of a sine or cosine function indicate?

Back

A negative coefficient indicates a reflection of the graph across the x-axis. For example, y = -2sin(x) reflects the standard sine wave downward.

Front

What is the relationship between the period and the coefficient of x in a sine or cosine function?

Back

The period (P) is calculated using the formula P = 2π/B, where B is the coefficient of x in the function. A larger B results in a shorter period.

Front

How can you identify the vertical shift of a sine or cosine function from its equation?

Back

The vertical shift can be identified from the equation in the form y = A sin(Bx) + D or y = A cos(Bx) + D, where D represents the vertical shift. If D is positive, the graph shifts up; if negative, it shifts down.

Front

What is the effect of changing the amplitude of a sine or cosine function?

Back

Changing the amplitude affects the height of the peaks and the depth of the troughs of the graph. A larger amplitude results in taller peaks and deeper troughs.

Front

How do you find the maximum and minimum values of a sine or cosine function?

Back

The maximum value of a sine or cosine function is equal to the amplitude plus the vertical shift, while the minimum value is the negative amplitude plus the vertical shift.